Study on the Lyapunov Stability of a Time-Discrete Macro Traffic System with Variable Delay and Feedback Control

This paper constructs and analyzes a time-discrete macro traffic system with bounded variable delay and feedback control strategy. By theoretical analysis using the Lyapunov theorem, a stable condition of the macro traffic system is derived under which traffic jams can be suppressed. The traffic developing properties of the new traffic system for different variable delay and feedback control parameters are illustrated through simulation. The results show that variable delay can easily lead a traffic system to evolve into a traffic jam, and the feedback control strategy can enhance the stability of the traffic system with respect to variable delay. Moreover, the traffic unstable level caused by variable delay is less than the unstable extent caused by the constant upper bound of variable delay; still it is more serious than the traffic fluctuation caused by the constant lower bound of variable delay.

A new fractional sliding mode controller based on nonlinear fractional-order proportional integral derivative controller structure to synchronize fractional-order chaotic systems with uncertainty and disturbances

This study presents a new fractional sliding mode controller based on nonlinear fractional-order proportional integral derivative controllers to synchronize fractional-order chaotic systems with uncertainties and affected by disturbance. According to the proposed control approach, a new fractional order control law is presented which ensures robust and stable synchronization of chaotic systems in the presence of uncertainties of the master and slave systems and bounded disturbance according to Lyapunov theorem. The proposed sliding mode controller is used to synchronize two non-smooth chaotic jerk systems affected by disturbance and uncertainty. Simulation results verify effectiveness and robustness of the proposed control law.

Synchronization methods for chaotic systems involving fractional derivative with a non-singular kernel.

This study considers the problem of control-synchronization for chaotic systems involving fractional derivative with a non-singular kernel. Using an extension of the Lyapunov Theorem for systems with Atangana-Baleanu-Caputo (ABC) derivative, a suitable control scheme is designed to achieve matrix projective synchronization (MP) between nonidentical ABC systems with different dimensions. The results are exemplified by the ABC version of the Lorenz system, Bloch system, and Liu system. To show the effectiveness of the proposed results, numerical simulations are performed based on the Adams-Bashforth-Mounlton numerical algorithm.

Simulation of Pose to Pose Moving of the Mobile Robot with Specified GPS Points

The applications of mobile robots in rescue scenarios, surviving to search, and exploration for outdoor navigation have received increasing attention due to their promising prospects. In this paper, a simulation of a differential wheeled mobile robot was presented, implementing a Global Positioning System (GPS) data points to specified starting points, final destination, and total error. In this work, a simple kinematic controller for polar coordinate trajectory tracking is developed. The tracking between two points, pose to pose, was specified by using the GPS data points. After that, the geodesy (GEO) formulation was used to convert the geodesy coordinate to Euclidean or polar coordinate. The Haversine equation obtained the distance between the two points. The system performance and stability of the tracking controller are proved using the Lyapunov theorem of the stability. A python script was used in this work as a simulator. Computer simulation with pose to pose trajectory strategy conform to the simplicity of the proposed controller.

Finite-Time Lyapunov Functions and Impulsive Control Design

In this paper, we introduce finite-time Lyapunov functions for impulsive systems. The relaxed sufficient conditions for asymptotic stability of an equilibrium of an impulsive system are given via finite-time Lyapunov functions. A converse finite-time Lyapunov theorem for controlling the impulsive system is proposed. Three examples are presented to show how to analyze the stability of an equilibrium of the considered impulsive system via finite-time Lyapunov functions. Furthermore, according to the results, we design an impulsive controller for a chaotic system modified from the Lorenz system.

The approach of partial stabilisation in design of discrete-time robust guidance laws against manoeuvering targets

ABSTRACTIn this paper, a robust three-dimensional guidance law against manoeuvering targets is designed using the approach of discrete-time partial stabilisation. In the proposed method, the equations of the guidance problem are divided into two subsystems where the asymptotic stability is desired only for the first one. The control input of the second subsystem is designed such that the collision to be ensured in a short time. Despite recent advances in technology and implementation of digital controllers, the design of guidance laws with the approach of discrete-time partial stabilisation has not been done, till now. One of the advantages of this paper is to design a discrete-time guidance law even with the difficulties of the discrete-time Lyapunov theorem. Moreover, the Lyapunov function is chosen based on the physics of the guidance problem (making the rate of line of sight (LOS) rotation close to zero), and it is shown that it is not possible to asymptotically stabilise the system in the case of manoeuvering targets. Nevertheless, to guarantee the collision with the target, it is enough to limit the rotation rate of LOS to a small value. Finally, simulation results are given to show the appropriate performance of the proposed guidance law.

New Robust Control Method Applied to the Locomotion of a 5-Link Biped Robot

SUMMARYThis paper proposes a new design of robust control combining feedback linearization, backstepping, and sliding mode control called FLBS applied to the locomotion of five-link biped robot. Due to the underactuated robot’s model, the system has a hybrid nature, while the FLBS control can provide a stabilized walking movement even with the existence of large disturbances and uncertainties by implementing smooth chatter-free signals. Stability of the method is proven using the Lyapunov theorem based on the hybrid zero dynamics and Poincaré map. The simulations show the controller performance such as robustness and chatter-free response in the presence of uncertainty and disturbance.